# PSAT Math : Pattern Behaviors in Exponents

## Example Questions

### Example Question #1 : How To Find Patterns In Exponents

Solve for

Possible Answers:

None of the above

Correct answer:

Explanation:

=

which means

### Example Question #253 : Exponents

Which of the following statements is the same as:

Possible Answers:

Correct answer:

Explanation:

Remember the laws of exponents. In particular, when the base is nonzero:

An effective way to compare these statements, is to convert them all into exponents with base 2. The original statement becomes:

This is identical to statement I. Now consider statement II:

Therefore, statement II is not identical to the original statement. Finally, consider statement III:

which is also identical to the original statement. As a result, only I and III are the same as the original statement.

### Example Question #3 : How To Find Patterns In Exponents

Write in exponential form:

Possible Answers:

Correct answer:

Explanation:

Using properties of radicals e.g.,

we get

### Example Question #4 : How To Find Patterns In Exponents

Write in exponential form:

Possible Answers:

Correct answer:

Explanation:

Properties of Radicals

### Example Question #11 : Pattern Behaviors In Exponents

Write in radical notation:

Possible Answers:

Correct answer:

Explanation:

Properties of Radicals

### Example Question #261 : Exponents

Express in radical form :

Possible Answers:

Correct answer:

Explanation:

Properties of Radicals

### Example Question #263 : Exponents

Simplify:

Possible Answers:

Correct answer:

Explanation:

### Example Question #11 : How To Find Patterns In Exponents

Simplify:

Possible Answers:

Correct answer:

Explanation:

Convert the given expression into a single radical e.g. the expression inside the radical is:

and the cube root of this is :

### Example Question #261 : Exponents

Solve for .

Possible Answers:

Correct answer:

Explanation:

Hence  must be equal to 2.

### Example Question #581 : Algebra

Simplify:

Possible Answers:

Correct answer:

Explanation:

Now

Hence the correct answer is